2 * Minimizing copies with an exact algorithm using mixed integer programming (MIP).
3 * Problem statement as a 'quadratic 0-1 program with linear constraints' with
4 * n binary variables. Constraints are knapsack (enforce color for each node) and
5 * cliques of ifg (interference constraints).
6 * Transformation into a 'mixed integer program' with n binary variables and
7 * additional 2n real variables. Constraints are the above the transformed
8 * objective function and 'complementary conditions' for two var classes.
11 * NOTE: Unfortunately no good solver is available locally (or even for linking)
12 * We use CPLEX 9.0 which runs on a machine residing at the Rechenzentrum.
27 #include "becopyopt.h"
28 #include "becopystat.h"
30 #undef DUMP_MATRICES /**< dumps all matrices completely. only recommended for small problems */
31 #define DUMP_MILP /**< dumps the problem as Mixed Integer Linear Programming in "CPLEX"-MPS format. NOT fixed-column-MPS. */
32 #undef DO_SOLVE /**< solve the MPS output with CPLEX */
33 #undef DELETE_FILES /**< deletes all dumped files after use */
35 /* CPLEX-account related stuff */
36 #define SSH_USER_HOST "kb61@sp-smp.rz.uni-karlsruhe.de"
37 #define SSH_PASSWD_FILE "/ben/daniel/.smppw"
38 #define EXPECT_FILENAME "runme" /** name of the expect-script */
40 #define DEBUG_LVL 0 //SET_LEVEL_1
41 static firm_dbg_module_t *dbg = NULL;
43 #define SLOTS_NUM2POS 256
44 #define SLOTS_LIVING 32
46 /* get_weight represents the _gain_ if node n and m have the same color. */
47 #define get_weight(n,m) 1
50 * A type storing names of the x variables in the form x[NUMBER]_[COLOR]
52 typedef struct _x_name_t {
57 * For each node taking part in the opt-problem its position in the
58 * x-variable-vector is stored in a set. This set maps the node-nr (given by
59 * benumb) to the position in the vector.
61 typedef struct _num2pos_t {
66 * A type storing the unmodified '0-1 quadratic program' of the form
72 * This problem is called the original problem
74 typedef struct _problem_instance_t {
75 const copy_opt_t *co; /** the original copy_opt problem */
76 int x_dim, A_dim, B_dim; /**< number of: x variables (equals Q_dim), rows in A, rows in B */
77 x_name_t *x; /**< stores the names of the x variables. all possible colors for a node are ordered and occupy consecutive entries. lives in obstack ob. */
78 set *num2pos; /**< maps node numbers to positions in x. */
79 sp_matrix_t *Q, *A, *B; /**< the (sparse) matrices of this problem */
81 /* needed only for linearizations */
82 int bigM, maxQij, minQij;
84 /* overhead needed to build this */
90 /* Nodes have consecutive numbers so this hash shoud be fine */
91 #define HASH_NUM(num) num
93 static int set_cmp_num2pos(const void *x, const void *y, size_t size) {
94 return ((num2pos_t *)x)->num != ((num2pos_t *)y)->num;
98 * Sets the first position of node with number num to pos.
99 * See x_name_t *x in _problem_instance_t.
101 static INLINE void pi_set_first_pos(problem_instance_t *pi, int num, int pos) {
105 set_insert(pi->num2pos, &find, sizeof(find), HASH_NUM(num));
109 * Get position by number. (First possible color)
110 * returns -1 if not found.
112 static INLINE int pi_get_first_pos(problem_instance_t *pi, int num) {
113 num2pos_t find, *found;
115 found = set_find(pi->num2pos, &find, sizeof(find), HASH_NUM(num));
117 assert(pi->x[found->pos].n == num && (found->pos == 0 || pi->x[found->pos-1].n != num) && "pi->num2pos is broken!");
124 * Get position by number and color.
125 * returns -1 if not found.
127 static INLINE int pi_get_pos(problem_instance_t *pi, int num, int col) {
128 num2pos_t find, *found;
132 found = set_find(pi->num2pos, &find, sizeof(find), HASH_NUM(num));
136 while (pos < pi->x_dim && pi->x[pos].n == num && pi->x[pos].c < col)
139 if (pi->x[pos].n == num && pi->x[pos].c == col)
147 * Dump the raw matrices of the problem to a file for debugging.
149 static void pi_dump_matrices(problem_instance_t *pi) {
151 FILE *out = ffopen(pi->co->name, "matrix", "wt");
153 DBG((dbg, LEVEL_1, "Dumping raw...\n"));
154 fprintf(out, "\n\nx-names =\n");
155 for (i=0; i<pi->x_dim; ++i)
156 fprintf(out, "%5d %2d\n", pi->x[i].n, pi->x[i].c);
158 fprintf(out, "\n\n-Q =\n");
159 matrix_dump(pi->Q, out, -1);
161 fprintf(out, "\n\nA =\n");
162 matrix_dump(pi->A, out, 1);
164 fprintf(out, "\n\nB =\n");
165 matrix_dump(pi->B, out, 1);
173 * Dumps an mps file representing the problem. This is NOT the old-style,
174 * fixed-column format. Some white spaces are important, in general spaces
175 * are separators, MARKER-lines are used in COLUMN section to define binaries.
177 //BETTER use last 2 fields in COLUMNS section. See MPS docu for details
178 static void pi_dump_milp(problem_instance_t *pi) {
180 const matrix_elem_t *e;
182 FILE *out = ffopen(pi->co->name, "milp", "wt");
184 DBG((dbg, LEVEL_1, "Dumping milp...\n"));
185 max_abs_Qij = pi->maxQij;
186 if (-pi->minQij > max_abs_Qij)
187 max_abs_Qij = -pi->minQij;
188 pi->bigM = pi->A_dim * max_abs_Qij;
189 DBG((dbg, LEVEL_2, "BigM = %d\n", pi->bigM));
191 matrix_optimize(pi->Q);
192 good_row = bitset_alloca(pi->x_dim);
193 for (i=0; i<pi->x_dim; ++i)
194 if (matrix_row_first(pi->Q, i))
195 bitset_set(good_row, i);
197 fprintf(out, "NAME %s\n", pi->co->name);
199 fprintf(out, "ROWS\n");
200 fprintf(out, " N obj\n");
201 for (i=0; i<pi->x_dim; ++i)
202 if (bitset_is_set(good_row, i))
203 fprintf(out, " E cQ%d\n", i);
204 for (i=0; i<pi->A_dim; ++i)
205 fprintf(out, " E cA%d\n", i);
206 for (i=0; i<pi->B_dim; ++i)
207 fprintf(out, " L cB%d\n", i);
208 for (i=0; i<pi->x_dim; ++i)
209 if (bitset_is_set(good_row, i))
210 fprintf(out, " L cy%d\n", i);
212 fprintf(out, "COLUMNS\n");
213 /* the x vars come first */
214 /* mark them as binaries */
215 fprintf(out, " MARKI0\t'MARKER'\t'INTORG'\n");
216 for (i=0; i<pi->x_dim; ++i) {
217 /* participation in objective */
218 if (bitset_is_set(good_row, i))
219 fprintf(out, " x%d_%d\tobj\t%d\n", pi->x[i].n, pi->x[i].c, -pi->bigM);
221 matrix_foreach_in_col(pi->Q, i, e)
222 fprintf(out, " x%d_%d\tcQ%d\t%d\n", pi->x[i].n, pi->x[i].c, e->row, e->val);
224 matrix_foreach_in_col(pi->A, i, e)
225 fprintf(out, " x%d_%d\tcA%d\t%d\n", pi->x[i].n, pi->x[i].c, e->row, e->val);
227 matrix_foreach_in_col(pi->B, i, e)
228 fprintf(out, " x%d_%d\tcB%d\t%d\n", pi->x[i].n, pi->x[i].c, e->row, e->val);
230 if (bitset_is_set(good_row, i))
231 fprintf(out, " x%d_%d\tcy%d\t%d\n", pi->x[i].n, pi->x[i].c, i, 2*pi->bigM);
234 fprintf(out, " MARKI1\t'MARKER'\t'INTEND'\n"); /* end of marking */
236 /* next the s vars */
237 for (i=0; i<pi->x_dim; ++i)
238 if (bitset_is_set(good_row, i)) {
239 /* participation in objective */
240 fprintf(out, " s%d_%d\tobj\t%d\n", pi->x[i].n, pi->x[i].c, 1);
242 fprintf(out, " s%d_%d\tcQ%d\t%d\n", pi->x[i].n, pi->x[i].c, i, -1);
245 /* next the y vars */
246 for (i=0; i<pi->x_dim; ++i)
247 if (bitset_is_set(good_row, i)) {
249 fprintf(out, " y%d_%d\tcQ%d\t%d\n", pi->x[i].n, pi->x[i].c, i, -1);
251 fprintf(out, " y%d_%d\tcy%d\t%d\n", pi->x[i].n, pi->x[i].c, i, 1);
254 fprintf(out, "RHS\n");
255 for (i=0; i<pi->x_dim; ++i)
256 if (bitset_is_set(good_row, i))
257 fprintf(out, " rhs\tcQ%d\t%d\n", i, -pi->bigM);
258 for (i=0; i<pi->A_dim; ++i)
259 fprintf(out, " rhs\tcA%d\t%d\n", i, 1);
260 for (i=0; i<pi->B_dim; ++i)
261 fprintf(out, " rhs\tcB%d\t%d\n", i, 1);
262 for (i=0; i<pi->x_dim; ++i)
263 if (bitset_is_set(good_row, i))
264 fprintf(out, " rhs\tcy%d\t%d\n", i, 2*pi->bigM);
266 fprintf(out, "ENDATA\n");
273 * Dumps the known solution to a file to make use of it
274 * as a starting solution respectively as a bound
276 static void pi_dump_start_sol(problem_instance_t *pi) {
278 FILE *out = ffopen(pi->co->name, "mst", "wt");
279 fprintf(out, "NAME\n");
280 for (i=0; i<pi->x_dim; ++i) {
284 if (get_irn_color(get_irn_for_graph_nr(pi->co->irg, n)) == c)
288 fprintf(out, " x%d_%d\t%d\n", n, c, val);
290 fprintf(out, "ENDATA\n");
295 * Invoke an external solver
297 static void pi_solve_ilp(problem_instance_t *pi) {
301 DBG((dbg, LEVEL_1, "Solving with CPLEX@RZ...\n"));
302 /* write command file for CPLEX */
303 out = ffopen(pi->co->name, "cmd", "wt");
304 fprintf(out, "set logfile %s.sol\n", pi->co->name);
306 fprintf(out, "read %s.milp mps\n", pi->co->name);
309 fprintf(out, "read %s.miqp mps\n", pi->co->name);
311 fprintf(out, "read %s.mst\n", pi->co->name);
312 fprintf(out, "set mip strategy mipstart 1\n");
313 fprintf(out, "set mip emphasis 3\n");
314 fprintf(out, "optimize\n");
315 fprintf(out, "display solution variables 1-%d\n", pi->x_dim);
316 fprintf(out, "set logfile cplex.log\n");
317 fprintf(out, "quit\n");
320 /* write expect-file for copying problem to RZ */
321 pwfile = fopen(SSH_PASSWD_FILE, "rt");
322 fgets(passwd, sizeof(passwd), pwfile);
325 out = ffopen(EXPECT_FILENAME, "exp", "wt");
326 fprintf(out, "#! /usr/bin/expect\n");
327 fprintf(out, "spawn scp %s.miqp %s.milp %s.mst %s.cmd %s:\n", pi->co->name, pi->co->name, pi->co->name, pi->co->name, SSH_USER_HOST); /* copy problem files */
328 fprintf(out, "expect \"word:\"\nsend \"%s\\n\"\ninteract\n", passwd);
330 fprintf(out, "spawn ssh %s \"./cplex90 < %s.cmd\"\n", SSH_USER_HOST, pi->co->name); /* solve */
331 fprintf(out, "expect \"word:\"\nsend \"%s\\n\"\ninteract\n", passwd);
333 fprintf(out, "spawn scp %s:%s.sol .\n", SSH_USER_HOST, pi->co->name); /*copy back solution */
334 fprintf(out, "expect \"word:\"\nsend \"%s\\n\"\ninteract\n", passwd);
336 fprintf(out, "spawn ssh %s ./dell\n", SSH_USER_HOST); /* clean files on server */
337 fprintf(out, "expect \"word:\"\nsend \"%s\\n\"\ninteract\n", passwd);
340 /* call the expect script */
341 chmod(EXPECT_FILENAME ".exp", 0700);
342 system(EXPECT_FILENAME ".exp");
346 * Sets the colors of irns according to the values of variables found in the
347 * output file of the solver.
349 static void pi_apply_solution(problem_instance_t *pi) {
350 FILE *in = ffopen(pi->co->name, "sol", "rt");
354 DBG((dbg, LEVEL_1, "Applying solution...\n"));
357 int num = -1, col = -1, val = -1;
359 fgets(buf, sizeof(buf), in);
360 DBG((dbg, LEVEL_3, "Line: %s", buf));
362 if (strcmp(buf, "No integer feasible solution exists.") == 0)
363 assert(0 && "CPLEX says: No integer feasible solution exists!");
365 if (strcmp(buf, "TODO Out of memory") == 0) {}
372 if (sscanf(buf, "Solution time = %f sec. Iterations = %d", &sol_time, &iter) == 2) {
373 DBG((dbg, LEVEL_2, " Time: %f Iter: %d\n", sol_time, iter));
374 curr_vals[I_ILP_TIME] += 10 * sol_time;
375 curr_vals[I_ILP_ITER] += iter;
381 if (sscanf(buf, "x%d_%d %d", &num, &col, &val) == 3 && val == 1) {
382 DBG((dbg, LEVEL_2, " x%d_%d = %d\n", num, col, val));
383 set_irn_color(get_irn_for_graph_nr(pi->co->irg, num), col);
388 #endif /* DO_SOLVE */
391 static void pi_delete_files(problem_instance_t *pi) {
393 int end = snprintf(buf, sizeof(buf), "%s", pi->co->name);
394 DBG((dbg, LEVEL_1, "Deleting files...\n"));
396 snprintf(buf+end, sizeof(buf)-end, ".matrix");
400 snprintf(buf+end, sizeof(buf)-end, ".mps");
402 snprintf(buf+end, sizeof(buf)-end, ".mst");
404 snprintf(buf+end, sizeof(buf)-end, ".cmd");
406 remove(EXPECT_FILENAME ".exp");
409 snprintf(buf+end, sizeof(buf)-end, ".sol");
416 * Collects all irns in currently processed register class
418 static void pi_collect_x_names(ir_node *block, void *env) {
419 problem_instance_t *pi = env;
420 struct list_head *head = &get_ra_block_info(block)->border_head;
422 bitset_t *pos_regs = bitset_alloca(pi->co->cls->n_regs);
424 list_for_each_entry_reverse(border_t, curr, head, list)
425 if (curr->is_def && curr->is_real) {
427 pi->A_dim++; /* one knapsack constraint for each node */
429 xx.n = get_irn_graph_nr(curr->irn);
430 pi_set_first_pos(pi, xx.n, pi->x_dim);
432 // iterate over all possible colors in order
433 bitset_clear_all(pos_regs);
434 pi->co->isa->get_allocatable_regs(curr->irn, pi->co->cls, pos_regs);
435 bitset_foreach(pos_regs, xx.c) {
436 DBG((dbg, LEVEL_2, "Adding %n %d\n", curr->irn, xx.c));
437 obstack_grow(&pi->ob, &xx, sizeof(xx));
438 pi->x_dim++; /* one x variable for each node and color */
444 * Checks if all nodes in living are live_out in block block.
446 static INLINE int all_live_in(ir_node *block, pset *living) {
448 for (n = pset_first(living); n; n = pset_next(living))
449 if (!is_live_in(block, n)) {
457 * Finds cliques in the interference graph, considering only nodes
458 * for which the color pi->curr_color is possible. Finds only 'maximal-cliques',
459 * viz cliques which are not conatained in another one.
460 * This is used for the matrix B.
462 static void pi_clique_finder(ir_node *block, void *env) {
463 problem_instance_t *pi = env;
464 enum phase_t {growing, shrinking} phase = growing;
465 struct list_head *head = &get_ra_block_info(block)->border_head;
467 pset *living = pset_new_ptr(SLOTS_LIVING);
469 list_for_each_entry_reverse(border_t, b, head, list) {
470 const ir_node *irn = b->irn;
473 DBG((dbg, LEVEL_2, "Def %n\n", irn));
474 pset_insert_ptr(living, irn);
476 } else { /* is_use */
477 DBG((dbg, LEVEL_2, "Use %n\n", irn));
479 /* before shrinking the set, store the current 'maximum' clique;
480 * do NOT if clique is a single node
481 * do NOT if all values are live_in (in this case they were contained in a live-out clique elsewhere) */
482 if (phase == growing && pset_count(living) >= 2 && !all_live_in(block, living)) {
484 for (n = pset_first(living); n; n = pset_next(living)) {
485 int pos = pi_get_pos(pi, get_irn_graph_nr(n), pi->curr_color);
486 matrix_set(pi->B, pi->curr_row, pos, 1);
487 DBG((dbg, LEVEL_2, "B[%d, %d] := %d\n", pi->curr_row, pos, 1));
491 pset_remove_ptr(living, irn);
500 * Generate the initial problem matrices and vectors.
502 static problem_instance_t *new_pi(const copy_opt_t *co) {
503 problem_instance_t *pi;
505 DBG((dbg, LEVEL_1, "Generating new instance...\n"));
506 pi = xcalloc(1, sizeof(*pi));
508 pi->num2pos = new_set(set_cmp_num2pos, SLOTS_NUM2POS);
512 * one entry per node and possible color */
513 obstack_init(&pi->ob);
514 dom_tree_walk_irg(co->irg, pi_collect_x_names, NULL, pi);
515 pi->x = obstack_finish(&pi->ob);
518 * weights for the 'same-color-optimization' target */
521 pi->Q = new_matrix(pi->x_dim, pi->x_dim);
523 list_for_each_entry(unit_t, curr, &co->units, units) {
524 const ir_node *root, *arg;
526 unsigned rootpos, argpos;
529 root = curr->nodes[0];
530 rootnr = get_irn_graph_nr(root);
531 rootpos = pi_get_first_pos(pi, rootnr);
532 for (i = 1; i < curr->node_count; ++i) {
533 int weight = -get_weight(root, arg);
534 arg = curr->nodes[i];
535 argnr = get_irn_graph_nr(arg);
536 argpos = pi_get_first_pos(pi, argnr);
538 DBG((dbg, LEVEL_2, "Q[%n, %n] := %d\n", root, arg, weight));
539 /* for all colors root and arg have in common, set the weight for
540 * this pair in the objective function matrix Q */
541 while (rootpos < pi->x_dim && argpos < pi->x_dim &&
542 pi->x[rootpos].n == rootnr && pi->x[argpos].n == argnr) {
543 if (pi->x[rootpos].c < pi->x[argpos].c)
545 else if (pi->x[rootpos].c > pi->x[argpos].c)
548 matrix_set(pi->Q, rootpos++, argpos++, weight);
550 if (weight < pi->minQij) {
551 DBG((dbg, LEVEL_2, "minQij = %d\n", weight));
554 if (weight > pi->maxQij) {
555 DBG((dbg, LEVEL_2, "maxQij = %d\n", weight));
565 * knapsack constraint for each node */
567 int row = 0, col = 0;
568 pi->A = new_matrix(pi->A_dim, pi->x_dim);
569 while (col < pi->x_dim) {
570 int curr_n = pi->x[col].n;
571 while (col < pi->x_dim && pi->x[col].n == curr_n) {
572 DBG((dbg, LEVEL_2, "A[%d, %d] := %d\n", row, col, 1));
573 matrix_set(pi->A, row, col++, 1);
577 assert(row == pi->A_dim);
581 * interference constraints using exactly those cliques not contained in others. */
583 int color, expected_clipques = pi->A_dim/4 * pi->co->cls->n_regs;
584 pi->B = new_matrix(expected_clipques, pi->x_dim);
585 for (color = 0; color < pi->co->cls->n_regs; ++color) {
586 pi->curr_color = color;
587 dom_tree_walk_irg(pi->co->irg, pi_clique_finder, NULL, pi);
589 pi->B_dim = matrix_get_rowcount(pi->B);
596 * clean the problem instance
598 static void free_pi(problem_instance_t *pi) {
599 DBG((dbg, LEVEL_1, "Generating new instance...\n"));
603 del_set(pi->num2pos);
604 obstack_free(&pi->ob, NULL);
608 void co_ilp_opt(copy_opt_t *co) {
609 problem_instance_t *pi;
611 dbg = firm_dbg_register("ir.be.copyoptilp");
612 firm_dbg_set_mask(dbg, DEBUG_LVL);
613 if (!strcmp(co->name, DEBUG_IRG))
614 firm_dbg_set_mask(dbg, -1);
617 DBG((dbg, 0, "\t\t\t %5d %5d %5d\n", pi->x_dim, pi->A_dim, pi->B_dim));
621 pi_dump_matrices(pi);
629 pi_dump_start_sol(pi);
631 pi_apply_solution(pi);